Feb 2 2012 - 12:00pm to 1:00pm
TSRB Banquet Hall
Title of Seminar: The Beauty of a Motion: Mathematical Definition, Robust Implementation and Applications to Design and Animation
We propose to measure the beauty of an affine motion by the inverse of its steadiness, which we define as its Average Relative Acceleration (ARA). Steady affine motions, for which ARA=0, include translations, rotations, rigid body screws, and the golden spiral. To facilitate the design of beautiful in-betweening motions that interpolate between an initial and a final pose (affine transformation), B and C, we propose the Steady Affine Morph (SAM), defined as AtB with A=CB–1. A SAM is affine-invariant and reversible. It preserves isometries (i.e., rigidity), similarities, and volume. Its velocity field is stationary both in the global and the local (moving) frames. Given a copy count, n, the series of uniformly sampled poses, Ai/nB, of a SAM form a regular pattern, which may be easily controlled by changing B, C, or n, and where consecutive poses are related by the same affinity A1/n. Although a real matrix At does not always exist, we show that it does for a convex and large subset of orientation-preserving affinities A. Our fast and accurate Extraction of Affinity Roots (EAR) algorithm computes At, when it exists, using closed form expressions in two or in three dimensions. We discuss SAM applications to pattern design and animation and to key-frame interpolation. In particular, we present a new curve subdivision scheme in the space of affine motions, which produces an apparently smooth, piecewise-steady motion that interpolates a given series of poses.
The talk describes joint work with Prof. Alvar Vinacua from UPC in Barcelona Spain. Reference: “Steady Afﬁne Motions and Morphs”, J. Rossignac and A. Vinacua. ACM Transactions on Graphics. SIGGRAPH 2012. Videos are posted at http://www.gvu.gatech.edu/~jarek/SAM
Jaroslaw (Jarek) Rossignac is a Full Professor in the College of Computing at Georgia Tech. His research focuses on the design, representation, simplification, compression, analysis and visualization of highly complex 3D shapes, structures, and animations. Before joining Georgia Tech in 1996 as the Director of the GVU Center, he was Senior Manager and Visualization Strategist at the IBM T.J. Watson Research Center. He holds a Ph.D. in E.E. from the University of Rochester, a Diplôme d'Ingénieur from the Ecole Nationale Supérieure en Électricité et Mécanique (ENSEM), and a Maîtrise in M.E. from the University of Nancy, France. He authored 26 patents and 133 peer-reviewed articles for which he received 23 Awards. He created the ACM Symposia on Solid Modeling and expanded them into the annual Solid and Physical Modeling (SPM) conferences; chaired 20 conferences and 6 international program committees; delivered over 30 Distinguished or Invited Lectures and Keynotes; and served on the Editorial Boards of 7 professional journals and on 74 Technical Program committees. Currently he heads the NSF Aquatic Propulsion Lab (APL) and the Modeling, Animation, Graphic, Interaction, and Compression (MAGIC) Lab at Georgia Tech, which hosts the Disney-sponsored Feature Animation Production Automation (FAPA) project. Rossignac is a Fellow of the Eurographics association and the Editor-in-Chief of GMOD (Graphical Models)